impression I got from the STATA manual was that you should only use panel corrected standard errors if the number of time periods is equal to, or greater, than the number of panels. In a study of the 50 states over 23 years, I would seem to violate this assumption. I asked Neal Beck about it and here is his reply, “PCSE’s work in this case. The only issue is T (i.e., time periods) being large enough (say over 15). Clearly you have that. FGLS (parks) does not work here, but you do not care.” In a subsequent message in which I asked about using PCSE’s with both random effects and fixed effects models, Beck replied as follows: “PCSE’S are totally orthogonal to the question of effects. For bigger T TSCS, re and fe are pretty similar. All the issues where re wins are for small T. But whether or not you need effects has literally nothing to with PCSES.” In a later e-mail Beck mentioned that panel corrected standard errors cannot really be done with random effects models.

Time Series Models

Dickey-Fuller Unit Root Test: dfuller loginc2, regress

Note: adding “regress” in the above command means you will receive the regression result in addition to the Dickey-Fuller test results Correlogram of ACF and PACF: corrgram loginc2

Note: to obtain pointwise confidence intervals try

the following: ac loginc2, needle (for ACF)

or: pac loginc2, needle (for PACF)

Also: for a correlogram on first differences try:

corrgram D.loginc2 (Note: there is no space between D. and loginc2)

ARIMA Models:

Structural (i.e., substantive independent variables with an arima error process with both one autoregressive and one moving average term) arima loginc2 dempreslag, ar(1) ma(1)

Non-Structural Model (i.e., current value of the dependent variable is entirely in terms of an autoregressive and moving average process) arima D.loginc2, ar(1) ma(1) (Note: no space between D. and loginc2) (for non-differenced dependent variable omit “D.”)

Bootstrapping (Jeffrey Harden, SPPQ,“A Bootstrap Method for Conducting Statistical Inference with Clustered Data.” State Politics & Policy Quarterly 11(2):223–246. The main drawback to using the BCSE method is that calculating the standard errors for a model multiple times will produce different estimates each time because different bootstrap samples are drawn each time. This leads to the question of how to report results in journal articles and presentations. This is an issue with any simulation-based technique, such as conventional bootstrapping

or Markov Chain Monte Carlo (MCMC) methods. The important points to note are that the analyst controls the number of simulations and adding more simulations brings the estimate closer to the true value. In the case of BCSE, increasing the number of bootstrap replications (B) shrinks the variation between calculations.1